Hydrogen Spectrum and Bohr’s Theory
Energies of electrons in atoms are quantized; this is evidenced by the emission (line) spectra of atoms.
Atoms of an element emit a unique set of specific wavelengths (spectral lines) that are the characteristic of that
element. Line spectra of elements are the elemental equivalent of fingerprints, because each element has a line
spectrum different from all of the other elements.
The energy levels and the spectrum of the hydrogen atom can be accounted for by using Bohr’s equation:
n = 1, 2, 3, – – – – – – -, ,
En = –RH / n2,
where RH = 2.179910–18 J is the Rydberg constant, and n is an integer, called the principal quantum number.
The spectral line of an atomic spectrum is produced when an electron absorbs energy and is excited to a
higher energy level. The excited state is not stable, thus the electron quickly returns to a lower energy state and
emits energy in the form of a photon, which is shown as a fine spectral line recorded on a photographic plate
(see Fig. 1). If one knows the energy of each level, the energy of transition from a higher level, Ei, to a lower
one, Ef, can be computed.
E = Ef – Ei = –RH (1/nf2 – 1/ni2)
where nf and ni are principal quantum numbers of the final and initial energy levels, respectively.
On the other hand, the energy of a photon is also proportional to the frequency, , which in turn is
inversely proportional to the wavelength, .
E = h = hc / ,
where h = 6.625610–34 J.s is the Planck’s constant and
c = 2.9979108 m/s is the speed of light
Rearranging Eq. (3), we obtain the wavelength of a hydrogen spectral line.
= hc / E ,
The value of hc can be pre-computed to give
= hc / E = (6.625610–34 J.s) (2.9979108 m/s) / (E)
= (1.986310–25 / E) m.J
= (1.986310–16 / E) nm.J
The computational steps of obtaining the wavelength is:
1. Calculate the energy levels, En, using Eq. (1)
2. Calculate the energy difference, E, of a given transition by using Eq. (2)
3. Substitute the E value into Eq. (5) to obtain the wavelength in the unit of nm.
1. Hydrogen Energy Levels
Calculate the first six energy levels of the hydrogen atom using Eq. (1) and insert the results in the right-hand side of Fig. 2.
Table 1. Energy levels of the hydrogen atom
Energy, En (J)
2. Wavelengths of the Hydrogen Spectrum
Calculate the wavelengths of the specified transitions in Table 2 using Equations (2) and (5).
n_initial –> n_final
Table 2. Wavelengths of the hydrogen spectral lines.
Energy difference, E (J) (use equation 2)
Wavelength (nm) (equation 5)
3. Identification of Transitions
3a. Identify the wavelengths of the spectral lines of hydrogen from Figure 1 and insert those values in column 1 of Table 3.
3b. Identify the corresponding transitions (wavelengths) of these spectral lines using Table 2 values.
i. Put the matched wavelengths from Table 2 in the second column of Table 3.
ii. Put the corresponding transitions from Table 2 in the third column of Table 3.
3c. Draw arrows for the transitions shown in table 3, from initial state (higher n value) to final state (lower n value) with
the arrow pointed down in Figure 2, and also fill in the blanks for the energy levels and corresponding energy values.
Estimate the ‘experimental’ wavelengths in Figure1 and put in Column 1. Get calculated wavelengths from Table 2 and match them with Column1 wavelengths.
Place corresponding transitions (example 4–> 2) from Table 2 into Column 3. Now we know which experimental wavelength corresponds to which transition.
Table 3. Hydrogen’s spectral lines and the calculated spectral lines and their corresponding transitions using the Bohr equation.
Wavelength (nm) of hydrogen’s
Calculated wavelength (nm)
spectral lines (from Fig. 1)
(from Table 2)
(from Table 2)
Use Table 1 data to fill in the below.
E n ( J)
n = En =
n = En =
n = En =
1. How well does the Bohr equation predict the line spectrum of hydrogen?
2. Which transition in table 3 emits the highest energy photon?
3. Which transition in table 3 emits the lowest energy photon?
4. Which transition in table 3 emits the highest energy photon in the visible region?
5. Which transition in table 3 emits the lowest energy photon in the visible region?
Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.
You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.Read more
Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.Read more
Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.Read more
Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.Read more
By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.Read more